# Answer to Question #372 in Statistics and Probability for Dong-Sun

Question #372

Student came to the exam knowing only 24 questions out of 30. If he doesn’t know the answer on a question he gets a second one. Student can pass the exam if he answers at least one question. What is the probability of passing the exam?

Expert's answer

There are two ways the student can pass the exam:

1 – the first given question is one of 24 he knows. The probability to get it is: P(1) = 24/30 = 0.8;

2 – the first given question is one of 6 he doesn’t know, but the second one is one of 24 he knows (note that there are 29 questions left). The probability to get them is: P(2) = 6/30 * 24/29 ≈ 0.17.

As these events are independent, the probability to pass the exam is: P = P(1) + P(2) ≈ 0.8 + 0.17 ≈ 0.97.

1 – the first given question is one of 24 he knows. The probability to get it is: P(1) = 24/30 = 0.8;

2 – the first given question is one of 6 he doesn’t know, but the second one is one of 24 he knows (note that there are 29 questions left). The probability to get them is: P(2) = 6/30 * 24/29 ≈ 0.17.

As these events are independent, the probability to pass the exam is: P = P(1) + P(2) ≈ 0.8 + 0.17 ≈ 0.97.

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